Cafe Mustache has free wi-fi that shuts off at 6pm every evening, as well as coffee drinks, sandwiches, vegan chili, and a bar that starts serving in the evening. Very close to the California blue line.
Sublime's menu is not huge but it does include two vegan maki. The Futo Veggie roll contains inari (fried soy skin), oshinko (pickled radish), marinated shiitake mushrooms, avocado, and cucumber. The other is Vanilla Potato Temp, a very sweet tempura yam roll. There is also a vegan appetizer, which is a slightly spicy seaweed salad. It's not an extensive vegan selection but it is a very delicious one, and the prices were very good, despite being next door to a barber shop that charges $17 for a buzz cut.
Stan's offers vegan donuts as a "specialty" donut. Get there early in the day if you want one, they tend to sell out by around 5.
This group doesn't explicitly call itself vegan but it's basically a seitan fan club. It looks like their events have vegan food. From their description:
"Chicago Gluten Gluttons will host fundraiser dine-outs featuring glutenous options with proceeds going towards autoimmune disease research."
Meetup page: http://www.meetup.com/Chicago-Gluten-Gluttons/
The Dill Pickle is a small, local grocery cooperative that is open to the public. Members get discounts on their groceries, and have the chance to volunteer to get even more discounts. Open every day.
There are clearly-marked vegan options on the menu but there are also some unmarked options, so be sure the ask about it. Technically they don't take reservations but if you have a large group you can call ahead, they're very accommodating. Cash only.
This cozy Polish diner is deceptively vegan-friendly. Even though it doesn't say it on the menu there are vegan options, there are secret vegan pierogi. They made a fresh batch of delicious vegan pierogi for us, and provided free samples of vegan potato pancakes as well.